East Asian mathematical journal

  • 제38권5호
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  • Pages.549-581
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  • 2022
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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COMMUTING STRUCTURE JACOBI OPERATOR FOR SEMI-INVARIANT SUBMANIFOLDS OF CODIMENSION 3 IN COMPLEX SPACE FORMS

  • KI, U-Hang (The National Academy of Sciences) ;
  • SONG, Hyunjung (Department of Mathematics Hankuk University of Foreign Studies)
  • 투고 : 2022.04.03
  • 심사 : 2022.05.13
  • 발행 : 2022.09.30
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초록

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form Mn+1(c), c≠ 0. We denote by S and R𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃(≠ 2c) and any vector fields X and Y on M. In this paper, we prove that M satisfies R𝜉S = SR𝜉 and at the same time R𝜉𝜙 = 𝜙R𝜉, then M is a Hopf hypersurface of type (A) provided that the scalar curvature s of M holds s - 2(n - 1)c ≤ 0.

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참고문헌

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